Spatio-temporal evolution of Hanle and Zeeman synthetic polarization in a chromospheric spectral line

Due to the quick evolution of the solar chromosphere, its magnetic field cannot be inferred reliably without accounting for the temporal variations of its polarized light. This has been broadly overlooked in the modelling and interpretation of the polarization due to technical problems (e.g., lack of temporal resolution or of time-dependent MHD solar models) and/or because many polarization measurements can apparently be explained without dynamics. Here, we show that the temporal evolution is critic for explaining the spectral-line scattering polarization because of its sensitivity to rapidly-varying physical quantities and the possibility of signal cancellations and attenuation during extended time integration. For studying the combined effect of time-varying magnetic fields and kinematics, we solved the 1.5D NLTE problem of the second kind in time-dependent 3D R-MHD solar models and we synthesized the Hanle and Zeeman polarization in forward scattering for the chromospheric {\lambda}4227 line. We find that the quiet-sun polarization amplitudes depend on the periodicity and spectral coherence of the signal enhacements produced by kinematics, but that substantially larger linear polarization signals should exist all over the solar disk for short integration times. The spectral morphology of the polarization is discussed as a combination of Hanle, Zeeman, dynamic effects and partial redistribution. We give physical references for observations by degrading and characterizing our slit time-series in different spatio-temporal resolutions. The implications of our results for the interpretation of the second solar spectrum and for the investigation of the solar atmospheric heatings are discussed.